Are sibling models a suitable tool in analyses of how reproductive factors affect child mortality?

Abstract

A mathematical argument 3 Methods 3.1 Estimation of effect parameters to use in the simulation 3.2 Simulation 3.3 Estimation of mortality models from the simulated population 3.4 Replications 4 Results 4.1 Assuming that there is no effect of earlier infant death on fertility 4.2 What happens if there 'in reality' is an effect of earlier infant death on fertility? 4.3 Generally higher fertility or mortality 4.4 Alternative assumptions about effects of maternal age, birth interval, and birth order in the simulation 4.5 Alternative assumptions about other relationships 4.6 Steps one might consider taking to solve the problem 5 Conclusion 6 Acknowledgements References

The effects of birth spacing on health and socioeconomic outcomes across the life course: evidence from the Utah Population Database

“…Families that experience multiple infant deaths are strongly selected, and this is particularly true in a low-mortality context. Recent research has also highlighted the possibility that offspring deaths change the fertility behavior of parents, meaning that the length of the birth interval itself is influenced by the death of the preceding sibling; when the outcome for one sibling influences the exposure for another, sibling fixed effects models may be biased (Sjölander et al, 2016;Kravdal, 2020). This is particularly likely for infant mortality, but may also be true for our analyses of LBW and preterm, and is an important limitation of the sibling comparison analyses.…”

Response to letter: Sibling models—An underused tool with limitations

“…A simulation has shown that the bias may be huge. 5 There is apparently inadequate awareness of the linear-dependence and…”

Effects of previous birth interval length on child outcomes can be estimated in a sibling analysis even when there are only two siblings

“…At each month (t) until the woman turned 45, probabilities of first (f 1tj ) and higher-order (f 2tj ) births were predicted from the logistic equations where A tj , D tj and P tj are categorical variables representing age, time since last birth, and parity, respectively, and σ j is the fertility random term. The coefficients (ie the αs and βs) were taken from an earlier study 13 and reflect patterns actually observed in Norway, but subjected to visual smoothing. The variables A tj , D tj , and P tj were updated monthly as the simulation "proceeded.…”

“…For each month, a number was drawn from a uniform distribution over [0,1], and if this number was smaller than the relevant predicted birth probability, a birth (up to a fifth, as few have more children in Norway) was assigned to the woman that month. In that case, the probability that this child died within 12 months was predicted from the relevant demographic variables multiplied by coefficients taken from the mentioned earlier study 13 (except that a larger intercept was used to get a larger number of deaths), and with a mortality random term added-in parallel with the predictions of fertility. In mathematical terms, the prediction equation for the death probability m ij for child i of mother j was:…”

“…This is because estimates from sibling models may actually be severely biased when a reproductive variable is the "exposure," and the "outcome" is mortality or something else that may affect subsequent fertility and thus the "exposure" for a younger sibling-a methodological problem that has only recently been acknowledged in the literature. 13 This has, of course, no implications for the conclusions that are drawn. The same picture would have appeared from the simulations if another outcome not affecting the "exposure" for younger siblings in the real world had been chosen.…”